High forces acting on a structure will cause things to break. So how high are the forces, or loads (as they’re generically called)? How hard can *predicting *loads be? Turns out, pretty difficult - enough for an entire aerospace discipline to be dedicated to only generating loads. The challenge is in the details: *how conservative is conservative enough? What physics are relevant to the structure? At what time do the loads apply? *These are exactly the types of questions a dynamicist will ask - if they’re interesting to you too, keep reading.

I’m hoping to shed some light on a field in aerospace engineering that’s a little more behind the scenes. Loads and dynamics guides vehicle design from cradle-to-grave, accomplished by generating detailed load cases that responsible engineers design their parts to withstand. No two days are alike as a dynamicist – it’s a fast-paced combination of building analysis models and testing those models against real hardware being manufactured in the factory. For example, we’ll take accelerometers (sensors that measure acceleration - the rate of change of speed) and put them on hardware to validate analytical models. We’ll also take flight and test stand data to validate the assumptions used to generate our load cases. This is highly detail-oriented, data-driven work that can become messy - but that’s what makes it fun in the first place. That’s what brought me to this field - I was working with data and making simulations for race cars in college, and I had the opportunity to do the same on rockets at several companies.

# A Brief Overview of Dynamics

Here’s an image you might’ve seen before, maybe in a textbook, or maybe it’s your first time seeing this at all. No worries, I’m just using it as an example from which we’ll start talking about some key aspects of dynamics.

There are just a few components to this diagram. First, we have a big block, representing some amount of mass. Think of it as the object we want to move. We also defined with the arrow pointing to the right, that the positive X-direction is to the right. This block can only move in one direction - horizontally. This constraint on the block's motion introduces the concept of degrees of freedom. A degree of freedom refers to an independent way in which a system can move or change. In this case, our block has only one degree of freedom, as it can only move along the x-axis, so we often call this system a single degree-of-freedom, or SDOF, system.

If we want to move the block, the red arrow represents a force that can be applied to the block, with a magnitude F. Newton's second law is F=ma, which tells us that the magnitude of acceleration is directly proportional to the force. The harder you push, the faster the speed changes. If you stop pushing, then the mass will continue at that same speed until something else acts on it.

Connected to the block are two “elements,” as we often call them. The one with the coils is a spring, like a slinky or rubber band. Springs don’t have a lot of surprises: if you stretch them away from their resting position, they’ll produce a force proportional to the amount they’ve been stretched. F = kx, also known as Hooke’s Law.

Now what’s that other element connected to the mass? That thing is called a damper, and you probably already have one on your car. Its main purpose is to resist changes in velocity. Moving a damper very slowly is easy, while trying to suddenly move a damper is difficult because the force a damper produces depends on its velocity.

If you put all three elements together, you get an equation that looks like this.

The left-hand side terms all represent the internal forces that are generated by the system. The mass produces a force proportional to its acceleration, the damper produces a force proportional to its velocity, and the spring produces a force proportional to its displacement. The dots on top of the x are a bit of notation meaning “time-derivative.” You start with displacement (no dots), whose derivative is velocity (one dot), and then whose derivative is acceleration (two dots). The right hand side term is the external force acting on the mass.

There are two important parameters in the single degree-of-freedom system: the natural frequency and the damping ratio. I won’t go deep into the math here, but think of the natural frequency being the amount of cycles this mass-spring-damper system would naturally oscillate at if you were to displace it and let go. A good analogy is a swingset, where the swing will always oscillate at the same speed, no matter how hard you push. The damping ratio is essentially a measure of energy dissipation in the system. As the damping ratio increases, energy is lost more quickly, and the system stops moving in a shorter period of time. High damping is good for reducing the amount of vibration seen at resonance, but it is difficult to precisely control the amount of damping inherent in a material. Dedicated devices like automotive dampers use oil moving through a series of valves to generate damping.

# How it Applies to Aerospace

This is all good stuff, and everything in aerospace dynamics starts from this simple idea of a single degree-of-freedom oscillator. The best example of this is in coupled loads analysis (CLA) as we’ll see here.

## Coupled Loads Analysis

Coupled loads analysis combines finite-element modeling, structural dynamics, and forcing functions to generate a set of loads to be used for vehicle-level design. The term generically refers to any loads analysis, but the name comes from taking a component, like a satellite, and combining it with a rocket model to generate a set of loads for the entire combined payload-launch vehicle system.

An example of a generic rocket model is shown above. You’ll notice that everything is kept pretty simple. Dynamicists will model the rocket and satellite as having multiple degrees of freedom and assemble an equation of motion with mass and stiffness **matrices**, combined with a displacement **vector**. Each degree of freedom will have its own natural frequency, so you can imagine the larger models will have thousands, if not millions of degrees of freedom.

The essential characteristics, like mass and stiffness are closely matched between the real world and this model. The model is divided up into a grid with elements and nodes, which are then used to solve for these mass and stiffness matrices.

For finite-element models, it is typical to remove high-frequency modes using one of two techniques: Guyan reduction (AKA "static condensation") or through the Craig-Brampton method. Removing high-frequency content is important because it can significantly reduce the amount of time it takes to do the analysis while maintaining accuracy for the lower frequency modes that are often of greater interest for loads (high frequency is covered by Environments in the next section). There are great resources online to dive into these techniques. I recommend starting with the NASA FEMCI website, which provides a great overview of some essential dynamic techniques: FEMCI Book - The Craig-Bampton Method (nasa.gov) .

All of this is used to size the “primary structure,” or the big things you can see, on the rocket. Loads will be delivered to the structural engineers designing the rocket, who will then do the strength calculations in their own models to see whether the structure can withstand these loads. If they do, then everyone is happy. If the structure can’t withstand the loads, then another round of iteration, on both the structural design and loads side, must be done to avoid issues in-flight.

## Environments

If you ever watch a rocket launch in-person, you’ll feel (and hear!) a deep rumble as you watch the rocket take off from the launchpad. Rockets are noisy! All that noise produced by a rocket affects the environment, both within the rocket as well as the surroundings. While we should be concerned with both, dynamicists primarily look at the vibration caused by acoustics within the payload bay, as well as within the rest of the rocket, which is why there’s an entire field dedicated to the vibration environment a rocket experiences throughout its life.

Many components on rockets are sensitive to vibration and shock. Fluid valves, a vital component of any vehicle, can get stuck or have their performance degraded by high vibration environments. Delicate electronics can be damaged by hard impacts or sustained high vibration levels, with the risk of circuit board components falling off or wiring becoming unplugged. Just look at this poor circuit board component sacrificed for this video:

It’s the job of an environments engineer to be able to predict these vibration environments and deliver them to designers so that their components can survive. Predictions are made using a combination of extrapolation from previous launch vehicle programs (ntrs.nasa.gov/api/citations/20100042567/downloads/20100042567.pdf), and analytical methods involving the finite-element method mentioned earlier as well as other fancier techniques. We’ll often deliver a vibration specification that looks something like the plot below. Essentially it is describing the energy, in terms of acceleration, across the frequency range of interest. This, in turn, can be translated into an equivalent acceleration that component designers analyze their parts to withstand. Dynamic environment engineers also recommend vibration isolation schemes and set minimum natural frequency targets for component designers to meet, with the intent of avoiding overlapping resonances that could cause damage.

After all that analysis, components must be tested to ensure they withstand that same environment. That profile is programmed into a shaker table, which is basically like a giant speaker that can precisely make the table move at the desired accelerations and frequencies in the specification. The part is then bolted down and shaken for the test, and signs of failure are monitored during the test. Sometimes you learn new things from shaker table testing, other times it’s much more boring. Some companies are doing this at an even larger scale, with Chinese rocket startup CAS Space shaking an entire portion of their rocket on an enormous shaker table:

All of this is the bread and butter of a dynamic environments engineer. Vibration levels are developed for components on the vehicle which then are used by designers to size their parts, and then those same components are tested on the shaker to see how they perform in real life. It’s an interesting combination between test and analysis, and no two days in the role are identical. I’ve enjoyed working closely with hardware designers to make their designs better, and I’ve really enjoyed being in the lab setting up instrumentation and watching my predictions line up with the measured reality. It’s hard to find a better combination of design influence and test in my opinion!

## Multibody Dynamics

Multibody dynamics, or MBD, is concerned with large-scale interactions between structures on the vehicle. For example, MBD teams might be concerned with modeling how the rocket will separate, or how the landing legs might deploy. The main challenges here are the inherent nonlinearities that need to be accounted for an accurate description of the physics involved. The tooling and software used to analyze multibody systems is often bespoke and relatively complex, and so will vary between launch service providers. MBD often interacts heavily with Guidance, Navigation, and Control (GNC) teams, using trajectory outputs to inform initial conditions for highly detailed multibody simulations.

Take stage separation as an example. Rocket Lab has this awesome video showing stage separation for an Electron launch:

A MBD engineer might be developing models to determine the amount of force required to separate the two stages, or modeling the relative displacements between the two stages as they move apart. Those outputs then guide the design by defining locations where components are allowed to be to avoid collisions as well as mechanism sizing with minimum force and stroke length requirements. On the input side, the MBD engineer is looking at the trajectory and the set of all possible initial conditions to predict all possible scenarios during this stage separation event.

# Getting a Start

With the field being so broad, it might seem daunting to break into the field as a college freshman or new grad. That isn’t necessarily the case, given a healthy amount of coursework, interest in the field, and willingness to use the web for information.

## Coursework

On the coursework side, there’s several foundational math skills you need:

**Linear Algebra**- understanding how to work with large interconnected linear systems is a vital skill when analyzing dynamic systems.**Differential Equations**- this is fundamental to dynamic systems since we’re working with derivatives of position variables.**Numerical Methods**- it’s often very hard to analytically solve Dynamics problems, so numerical computing is used instead.

Because loads are coupled to structures and the design of vehicles, a strong foundation in mechanical design is essential. For example, you should know the fundamentals of solid mechanics, often covered in a second-year course in Mechanical Engineering, as well as machine element design that is typically covered with Shigley’s Introduction to Mechanical Design. On the dynamics side, you should have a strong foundation by taking a course in planar dynamics, as well as extending that into 3D dynamics. At my undergrad school, there is a course called System Dynamics that essentially unifies dynamic models across all major domains - electrical, thermal, mechanical, and fluid.

## Extracurriculars (And My Story)

Outside of class, I was responsible for the vehicle dynamics of our Formula SAE vehicles. Specifically, I analyzed both yaw and vertical dynamics of the vehicle, from tire and vehicle stability to suspension response. In the Formula SAE/Student world, dynamics are very often represented by lumped-mass elements. I started with simple models: quarter car models representing one corner of the suspension, single-track yaw models, and steady-state aerodynamic loading, all built in Python underlying our vehicle analysis codebase. This contained tools for lap time simulation, sensitivity studies, and several performance metrics for the vehicle - all of which were instrumental in helping design a world-class Formula Student vehicle.

A strong understanding of MBD and coupled dynamic systems was essential in developing our mechanical models for the vehicle. Despite being largely lumped-mass, complexity was added through coupling dynamic models to each other, with force outputs derived from state variables used as inputs to other models, and reaction forces fed back through forcing function inputs. This is all largely done ‘under the hood’ in visual tools in Simulink, but there are added benefits to understanding the signal flow when programming it, as well as being able to leverage existing software development toolchains (git, test runners, and CI/CD) to improve development efficiency. It also helps that Python is free, which is why several large aerospace companies are either switching to, or have already switched to Python for analysis tools.

Similar principles and tooling apply in a launch vehicle setting. Many, many things are different - the nature of the problem (going fast for the sake of going fast vs. taking payloads into space), the scale of projects (room-sized to building-sized), and the extremes involved (low-G to several dozen G), but the same governing equations all apply. On a program management side, technical risks must be balanced with program objectives and analysis sometimes needs to be scrappy to meet timeline requirements. Being a good dynamics engineer involves having the right judgment to use the correct level of analysis for the given hardware maturity and needs of a program at that point in time - not an easy task at all!

## Internships

The best launchpad I had into this industry was through an internship at a private rocket company. From my point of view, it doesn't really matter where you do an internship in dynamics, as long as you have strong mentors who will help you succeed in your role and help you learn about the field since it's impossible to learn everything you need to know from school.

I know that landing an internship is difficult, and I'll be the first to say that I had help from alumni in industry who reached out and asked if I wanted to intern at their company. I know that’s a rare privilege to have. My recommendation is to understand the role of a dynamics engineer and communicate that as you complete your application, whether that's through the way you tailor your resume or in the cover letter you submit. In the interview, be rock-solid on the fundamentals and know why you're interested in dynamics.

Don't be discouraged if you don't land an internship at a major aerospace company right away. Smaller companies, research labs, or even related industries can provide valuable experience. The skills you learn will be transferable, making you a stronger candidate for future aerospace positions.

If you're having trouble finding opportunities, consider reaching out to professors who might have industry connections or research projects related to dynamics or mechanical vibrations. Take advantage of career fairs and industry events at your school to network with professionals and learn about internship opportunities.

# Conclusion

As we've explored throughout this article, the field of loads and dynamics in aerospace engineering is an engaging blend of physics, mathematics, and real-world problem-solving. From the fundamental principles of single degree-of-freedom systems to the complex world of coupled loads analysis and multibody dynamics, this discipline forms the backbone of vehicle design and mission success.

The role of a dynamicist is far from boring. One day, you might be developing intricate finite element models to predict how a rocket will behave during launch. The next, you could be in a lab, setting up accelerometers on actual hardware to validate your analytical predictions. Moreover, the impact of dynamics is tangible and far-reaching. Analyses directly influence critical design decisions, from the overall architecture of a launch vehicle to the details of component design. It’s not just number crunching; it’s helping to shape the very spacecraft that will push the boundaries of human exploration.

For those considering a career in this field, the path may seem daunting, but it's also incredibly exciting. Whether you're coming from a background in mechanical engineering, aerospace, or even fields like automotive or civil engineering, the fundamental principles of dynamics provide a common language. Your journey might start with mastering the basics of linear algebra and differential equations, but it could lead you to designing the next generation of spacecraft or launch vehicles.

In the end, being a dynamicist in the aerospace industry is about more than just understanding forces and vibrations. It's about being a problem solver, a collaborator, and an innovator. It's about having the unique ability to see how seemingly small changes can have massive implications for an entire system. And perhaps most importantly, it's about playing a crucial role in humanity's ongoing quest to reach for the stars.

So whether you're a student just starting your academic journey, a professional considering a career change, or simply someone fascinated by the complexities of spaceflight, I encourage you to delve deeper into the world of dynamics. The challenges are significant, but the rewards – both intellectual and practical – are truly out of this world.

# Additional Resources

Some more fundamentals and short, digestible papers can be found on Tom Irvine’s website, Vibrationdata. He goes into the theory at a deeper level than what I’ve presented here, but also at an accessible level for anyone to understand. Some content is free, while some other content is paid-for. All the free content is already a great start into some of the more complex topics in dynamics. One important document on his website actually comes from NASA, which is the handbook used for Dynamic Environments, NASA-HDBK-7005. It goes into more detail than I was able to go into as to how dynamic levels are derived, how safety factors are applied, and how the test process works.

For general rocket knowledge, NASA has a trove of old papers dating back to the 1960s and beginning of manned spaceflight at the NASA Technical Reports Server (NTRS). This is where you can find information on turbopumps, SLS development, Apollo history - you name it!

For some tools already written in Python, Tim Widrick of NASA has published a library called pyyeti that implements some common routines used in structural dynamics. The examples are quite well documented, and I’ve found a lot of useful functions that I use in my day-to-day.

If you enjoyed this article or have any comments, feedback, or questions, please email us at admin@theoverview.org. Thanks for reading!

Aaron Fang